It is known to use catadioptric Fresnel-type lenses including a catadioptric portion consisting of a plurality of two-faceted prisms as, for example, disclosed in a summary on "TIR FRESNEL LENSES" by Dr. Lawrence W. James, reported on pages 215-221 of the proceedings for the Tenth Photovoltaic Concentrator Project Integration Meeting, Albuquerque, New Mexico, Apr. 6 & 7, 1983 and prepared by Sandia National Laboratories. Each prism has a refractive surface and a reflective surface, to form the lenses' structured surfaces to refract and reflect light from a light source striking those structured surfaces. In addition, such lenses have included conventional Fresnel-type portions at their center and terminating where the efficiency of the conventional portions approaches the efficiency of the catadioptric portions of the lenses. However, such lenses have suffered from the inability of the radial outer peripheral prisms in the catadioptric portions to properly refract all of the light incident upon each refractive surface at high incident angles to be internally reflected by each reflective surface. Thus, because of the high incident angles required at large radii, much of the light is lost. As a practical matter, this inability restricts the lenses' speeds, (i.e. F/numbers), or the efficiency of large angle bending of light rays.